Showing papers on "Feedback linearization published in 2002"

WMR control via dynamic feedback linearization: design, implementation, and experimental validation

Abstract: The subject of the paper is the motion control problem of wheeled mobile robots (WMRs) in environments without obstacles. With reference to the popular unicycle kinematics, it is shown that dynamic feedback linearization is an efficient design tool leading to a solution simultaneously valid for both trajectory tracking and setpoint regulation problems. The implementation of this approach on the laboratory prototype SuperMARIO, a two-wheel differentially driven mobile robot, is described in detail. To assess the quality of the proposed controller, we compare its performance with that of several existing control techniques in a number of experiments. The obtained results provide useful guidelines for WMR control designers.

Control of a quadrotor helicopter using visual feedback

Abstract: We present control methods for an autonomous four-rotor helicopter, called a quadrotor, using visual feedback as the primary sensor The vision system uses aground camera to estimate the pose (position and orientation) of the helicopter Two methods of control are studied - one using a series of mode-based, feedback linearizing controllers, and the other using a backstepping-like control law Various simulations of the model demonstrate the implementation of feedback linearization and the backstepping controllers Finally, we present initial flight experiments where the helicopter is restricted to vertical and yaw motions

Control of an optical fiber scanner

Abstract: Controls for an optical scanner, such as a single fiber scanning endoscope (SFSE) that includes a resonating optical fiber and a single photodetector to produce large field of view, high-resolution images. A nonlinear control scheme with feedback linearization is employed in one type of control to accurately produce a desired scan. Open loop and closed loops controllers are applied to the nonlinear optical scanner of the SFSE. A closed loop control (no model) uses either phase locked loop and PID controllers, or a dual-phase lock-in amplifier and two PIDs for each axis controlled. Other forms of the control that employ a model use a frequency space tracking control, an error space tracking control, feedback linearizing controls, an adaptive control, and a sliding mode control.

Feedback linearization of an active magnetic bearing with voltage control

Abstract: A feedback linearization controller is presented for a single-degree-of-freedom (DOF) magnetic bearing test rig. The feedback linearization controller is derived from a detailed nonlinear electromagnet model using both analytic relationships and experimental calibration data. The controller is implemented on the test rig in voltage mode, and measured open-loop transfer functions are used to demonstrate the effectiveness of the feedback linearization controller in transforming the nonlinear system to a linear plant. Next, a high-performance controller for the feedback linearized plant is designed with /spl mu/-synthesis to guarantee a beam compliance performance specification. A common problem associated with voltage control in magnetic suspensions and coil resistance variation, is successfully handled by augmenting the feedback linearized plant with a structured uncertainty. Experimental results demonstrate that the /spl mu/ controller with feedback linearization achieves the performance specified during design for the nonlinear plant independent of the disturbance force level or displacement incurred.

A nonlinear speed control for a PM synchronous motor using a simple disturbance estimation technique

Abstract: A nonlinear speed control for a permanent-magnet (PM) synchronous motor using a simple disturbance estimation technique is presented. By using a feedback linearization scheme, the nonlinear motor model can be linearized in the Brunovski canonical form, and the speed controller can be easily designed based on the linearized model. This technique, however, gives an undesirable output performance under the mismatch of the system parameters and load conditions. An adaptive linearization technique and a sliding-mode control technique have been reported. Although good performance can be obtained, the controller designs are quite complex. To overcome this drawback, the controller parameters are estimated by using a disturbance observer theory where the disturbance torque and flux linkage are estimated. Since only the two reduced-order observers are used for the parameter estimation, the observer designs are considerably simple and the computational load of the controller for parameter estimation is negligibly small. The nonlinear disturbances caused by the incomplete linearization can be effectively compensated by using this control scheme. Thus, a desired dynamic performance and a zero steady-state error can be obtained. The proposed control scheme is implemented on a PM synchronous motor using a digital signal processor (TMS320C31) and the effectiveness is verified through the comparative simulations and experiments.

Input-output linearization of retarded non-linear systems by using an extension of Lie derivative

Abstract: This paper considers the input-output linearization problem for retarded non-linear systems, which have time-delays in the state. By using an extension of the Lie derivative for functional differential equations, we derive a coordinates transformation and a static state feedback to obtain linear input-output behaviour for a class of retarded non-linear systems. The obtained coordinates transformation is allowed to contain not only the current value of the state variables but also the past values of ones. In addition, we show that the coordinates transformation is invertible in a neighbourhood of the origin and examine the stability condition of the closed loop system with the static state feedback. The effectiveness of the proposed technique is demonstrated through numerical simulations.

Feedback coding for information-based control: operating near the data-rate limit

Abstract: The paper begins with a restatement and proof of a tight bound on the data capacity a feedback channel must provide in order to stabilize a tight half-plane pole. This sets the stage for a treatment of some of the issues arising in the source coding of signals between controllers and plants in systems where feedback loops are closed using bandwidth limited communication links. In particular, we are interested in the qualitative dynamics of LTI feedback systems operating near the data-rate limit.

Brief Paper Robust control of nonlinear systems with parametric uncertainty

Abstract: Probabilistic robustness analysis and synthesis for nonlinear systems with uncertain parameters are presented. Monte Carlo simulation is used to estimate the likelihood of system instability and violation of performance requirements subject to variations of the probabilistic system parameters. Stochastic robust control synthesis searches the controller design parameter space to minimize a cost that is a function of the probabilities that design criteria will not be satis4ed. The robust control design approach is illustrated by a simple nonlinear example. A modi4ed feedback linearization control is chosen as controller structure, and the design parameters are searched by a genetic algorithm to achieve the tradeo7 between stability and performance robustness. ? 2002 Elsevier Science Ltd. All rights reserved.

Observer linearization by output-dependent time-scale transformations

Abstract: We study the problem of observer linearization for single-output dynamical systems in the presence of output-dependent time-scaling changes. An alternative algorithm for the solution of the observer linearization problem is introduced. The algorithm employs an exterior calculus approach that provides a simple procedure for the solution of the observer linearization problem by means of an output dependent time-scale transformation.

Ultra precision motion control of a multiple degrees of freedom magnetic suspension stage

Abstract: A general framework for ultra precision motion control of magnetic suspension actuation systems with large travel ranges in multiple degrees of freedom (DOF) is presented It encompasses the development of nonlinear electromagnetic force model for 6-DOF actuation, and the design of the necessary control architecture for ultra precision motion control of magnetic suspension actuation systems A 6-DOF magnetic suspension stage (MSS) was designed and fabricated to illustrate the developed framework The MSS consists of multiple electromagnets that are located around the flotor and are utilized to suspend and modulate its position and orientation The control architecture takes the six control parameters provided by a laser measuring system and intends to control the 6-DOF motion by regulating the current in the electromagnets The developed robust nonlinear control architecture consists of three components: 1) feedback linearization; 2) force distribution; and 3) H/sub /spl infin// robust controllers for each DOF of motion Several experiments are designed to illustrate the desired characteristics of the developed system

Robust switching adaptive control of multi-input nonlinear systems

Abstract: During the last decade a considerable progress has been made in the design of stabilizing controllers for nonlinear systems with known and unknown constant parameters. New design tools such as adaptive feedback linearization, adaptive back-stepping, control Lyapunov functions (CLFs) and robust control Lyapunov functions (RCLFs), nonlinear damping and switching adaptive control have been introduced. Most of the results developed are applicable to single-input feedback-linearizable systems and parametric-strict-feedback systems. These results, however, cannot be applied to multi-input feedback-linearizable systems, parametric-pure-feedback systems and systems that admit a linear-in-the-parameters CLF. In this paper, we develop a general procedure for designing robust adaptive controllers for a large class of multi-input nonlinear systems. This class of nonlinear systems includes as a special case multi-input feedback-linearizable systems, parametric-pure-feedback systems and systems that admit a linear-in-the-parameters CLF. The proposed approach uses tools from the theory of RCLF and the switching adaptive controllers proposed by the authors for overcoming the problem of computing the feedback control law when the estimation model becomes uncontrollable. The proposed control approach has also been shown to be robust with respect to exogenous bounded input disturbances.

Design and control for an electromagnetically driven X–Y–θ stage

Abstract: In this paper, the design and control of a novel precision motion stage is presented. It combines a flexural stage, electromagnetic actuation, capacitance position measurement, and nonlinear digital feedback control. This system has high open loop stiffness, and such a spring-dominated regime design provides a sufficient phase margin for applying phase lag-based control to reduce environmental effects such as base vibration and high frequency noises. In addition, the incorporation of the rotational motion not only increases the degree of freedom, but also provides capability for correcting possible undesired coupling between major axes. As a result, there would be fewer requirements in degree of precision for stage machining and assembly. With nonlinear control, the performance of this stage would be more consistent than those with controller based on linearizing system dynamics. Experiments show that the system has a bandwidth of 85 Hz with a minimum resolution of 50 nm, which is dominated by the quantization of data acquisition devices. This implies that the present design can be readily modified to achieve higher performance. However, it is also found that a major difficulty in the present design is the insufficient damping of the rotational mode, which limits the applicable control gain and achievable performance and should be corrected by proper mechanical redesign in the future. Nevertheless, this design still shows its potential advantages. Finally, the stage is integrated with a stylus to demonstrate the possible application in surface morphology measurement. Possible applications also include the fine motion control and scientific instrumentation.

Neural-network-based adaptive control for induction servomotor drive system

Abstract: A neural-network-based adaptive control (NNAC) design method is proposed to control an induction servomotor. In this NNAC design, a neural network (NN) controller is investigated to mimic a feedback linearization control law; and a compensation controller is designed to compensate for the approximation error between the feedback linearization control law and the NN controller. The interconnection weights of the NN can be online tuned in the sense of the Lyapunov stability theorem; thus, the stability of the control system can be guaranteed. Additionally, in this NNAC system design, an error estimation mechanism is investigated to estimate the bound of approximation error so that the chattering phenomenon of the control effort can be reduced. Simulation and experimental results show that the proposed NNAC servomotor control systems can achieve favorable tracking and robust performance with regard to parameter variations and external load disturbances.

Stabilization and coordination of underwater gliders

Abstract: An underwater glider is a buoyancy-driven, fixed-wing underwater vehicle that redistributes internal mass to control attitude. We examine the dynamics of a glider restricted to the vertical plane and derive a feedback law that stabilizes steady glide paths. The control law is physically motivated and with the appropriate choice of output can be interpreted as providing input-output feedback linearization. With this choice of output, we extend the feedback linearization approach to design control laws to coordinate the gliding motion of multiple underwater gliders.

Cable suspended robots: feedback controllers with positive inputs

Abstract: Cable-suspended robots are structurally similar to parallel actuated robots but with the fundamental difference that cables can only pull the end-effector but not push it. From a scientific point of view, this feature makes feedback control of cable-suspended robots a lot more challenging than their counterpart parallel-actuated robots. This paper describes the structure of two closed-loop asymptotic controllers that assure positive cable tensions. These controllers are based on the Lyapunov design technique and feedback linearization, respectively. The effectiveness of the approach is demonstrated through simulation and experiments on a six degree-of-freedom cable suspended robot.

Smooth output feedback stabilization of planar systems without controllable/observable linearization

Abstract: This note considers the problem of global stabilization by output feedback for a family of planar systems whose Jacobian linearization is neither controllable nor observable. The problem cannot be dealt with by existing output feedback design methods-most of them are based on the separation principle. Under appropriate growth conditions, we propose an output feedback control scheme that does not rely on the separation principle and achieves global asymptotic stabilization. The novelty of our control scheme lies in the explicit design of a dynamic output compensator, which combines a nonlinear-gain observer design and the technique of adding a power integrator. As a consequence, an interesting global stabilization result by output feedback can be obtained for feedback linearizable systems in a triangular form, which turns out to be new even in the two-dimensional case.

Control of high-order nonholonomic systems in power chained form using discontinuous feedback

Abstract: Addresses the problems of almost-asymptotic stabilization and global asymptotic regulation (GAR) for a class of high-order nonholonomic systems in power-chained form. This particular class of nonlinear systems is an extension of a nonholonomic system in chained form that has received considerable attention in the past few years. The nonholonomic system considered in this paper is not necessarily affine in the control variables and therefore cannot be handled by existing methods. Sufficient conditions are presented under which a discontinuous state-feedback control law (or a switching controller) can be recursively constructed, using the so-called "adding a power integrator" technique of C. Qian et al. (2001). We also illustrate how the results can be extend to multi-input systems in power-chained form. Simulation examples are provided to demonstrate the effectiveness of the proposed controllers.

Output Feedback Form and Adaptive Stabilization of a Nonlinear Aeroelastic System

Abstract: The question of output feedback representation and the design of a new adaptive control system for the control of an aeroelastic system using a single output feedback are treated. The chosen dynamic model describes the nonlinear plunge and pitch motion of a wing. The parameters of the system are assumed to be completely unknown. For the derivation of control law, the existence of output feedback forms of the model is examined. It is shown that for the choice of pitch angle as an output, an output feedback form of the system can be derived, but this kind of representation is not possible if the plunge displacement is chosen as an output. As such, adaptive control of the aerolastic model based on the backstepping design technique by plunge displacement feedback is not feasible. Then a global diffeomorphism is constructed for obtaining an output feedback form'of the model when the pitch angle is the output. Based on this output feedback form and a backstepping design technique, an adaptive control law for the trajectory control of the pitch angle is derived. For the synthesis of the controller, only the pitch angle is used. It is shown that, in the closed-loop system, pitch angle trajectory control is accomplished and that the state vector asymptotically converges to the origin in spite of the uncertainties in the model using only pitch angle feedback.

Global stabilization of cascade systems by C/sup 0/ partial-state feedback

Abstract: This paper shows how the nonsmooth but continuous feedback design approach developed recently for global stabilization of nonlinear systems with uncontrollable unstable linearization, and the notion and properties of the input-to-state stability Lyapunov function can be effectively coupled, resulting in globally stabilizing C/sup 0/ partial-state feedback controllers for a class of cascade systems which may not be smoothly stabilizable, even locally